Rapid receiver training is key for the efficient design of many communication systems. For example for voiceband modems, rapid start-up is greatly desirable. In systems where burst-mode transmission is employed, as in upstream transmission in two-way hybrid fiber coax cable TV (HCF-CATV) systems, fast acquisition of the adjustable receiver parameters using only short preambles allows the minimization of communication overhead.
Among various methods that have been proposed to simplify or otherwise improve rapid receiver training, several rely on the utilization of periodic, or cyclic, training sequences. This is described in, for example, K. H. Mueller et al. xe2x80x9cCyclic equalizationxe2x80x94A new rapidly converging equalization technique for synchronous data communicationxe2x80x9d, B.S.T.J., Vol 54No 2, pp. 369-406, February 1975 and S. Qureshi, xe2x80x9cFast start-up equalization with periodic training sequencesxe2x80x9d, IEEE Trans. on Inform. Theory, Vol. IT 23, pp. 553-563, September 1977. Specific periodic sequences can be obtained from pseudo-random sequences, chirp sequences, constant amplitude zero auto-correlation (CAZAC) sequences, or other suitable sequences.
The properties of the employed sequences are exploited at the receiver for fast calculation of estimates of adjustable receiver parameters. Initial estimates are then refined during subsequent receiver operations using adaptive adjustment methods.
The fast acquisition of carrier-frequency offset is a problem that generally coexists with the problems of fast equalizer computation. According to P. R. Chevillat et al, xe2x80x9cRapid Training of a Voiceband Data-Modem Receiver Employing an Equalizer with fractional-T Spaced Coefficientsxe2x80x9d, IEEEE Trans on Commun, Vol. COM-35, No 9, pp. 869-876, September 1987, both problems are solved by using a short cyclic preamble containing a CAZAC sequence. The method according to Chevillat et at, (the xe2x80x9cChevillat methodxe2x80x9d) is, however, limited to those cases for which the carrier-frequency offset does not exceed in absolute value 1/2MT Hz, assuming that one period of the CAZAC sequence extends over M symbol intervals T.
Let us denote the rate at which the transmit symbols are generated as 1/T and assume that the received signal is sampled at a rate of q times per symbol interval T, with q being an integer. The signal samples are fed into the delay line of an equalizer with a T/q tap spacing. We assume as well that we have an equalizer with a fractional-T tap spacing i.e., T/q tap spacing with q greater than 1. Following the notation found in the glossary attached, which may be found in Chevillat et al., the samples in the equalizer delay line at time nT are given by
xnq-i=unq-ixc2x7ej2xcfx80xcex94f(nq-i)T/q, 
i=0, 1, . . . , Mqxe2x88x921xe2x80x83xe2x80x83(1)
where we have assumed that the delay line has a total time span of MT. In the above equation, unq-i denotes the transmit signal after filtering by the channel transfer function and sampling, and xcex94f is an unknown carrier-frequency offset. The effect of noise has been ignored.
For fast receiver training, a cyclic preamble, obtained from the repetition of a specific symbol sequence of duration MT, is transmitted. In this case, the training signal has spectral lines spaced at intervals of 1/MT Hz. Also one full period of the channel output signal is always stored in the equalizer delay line. This can be used to efficiently compute the values of the equalizer coefficients needed at the receiver, as explained, e.g., in Mueller et al, Qureshi and Chevillat et al.
According to the Chevillat method, the periodic nature of the preamble is further exploited to produce an estimate of the carrier-frequency offset xcex94f. The Chevillat method utilizes the fact that once a full period of the channel output signal is found in the equalizer delay line, then
unq-Mq-i=unq-ixe2x80x83xe2x80x83(2)
and the samples entering and leaving the equalizer delay line only differ in a phase rotation of 2xcfx80xcex94fMT. Since phase-difference magnitudes larger than xcfx80 cannot be distinguished, this requires that phase rotation induced by carrier-frequency offset satisfies the following equation,
|2xcfx80xcex94fMT| less than xcfx80, xe2x80x83xe2x80x83(3)
which implies that the carrier frequency offset must be limited to                               "LeftBracketingBar"                      Δ            f                    "RightBracketingBar"                 less than                               1                          2              ⁢                              xe2x80x83                            ⁢              MT                                .                                    (        4        )            
Therefore, what is needed is a method which permits the acquisition of carrier-frequency offsets significantly larger than 1/2MT, but which use the same cyclic preamble.
A method, encoded in a logic medium, is provided which determines a carrier-frequency offset in an output signal of a transmission system. The transmission system uses a periodic training sequence having an associated spectrum. Given a measured spectral characteristic of an overall channel and an ideal spectral characteristic, the method is able to calculate an estimate of carrier-frequency offset by performing two acts. In a first act, the method determines a frequency shift in the overall channel characteristic by obtaining a spectral characteristic of the measured channel. In a second act, the method utilizes the amount by which the measured spectral characteristic is shifted with respect to the ideal spectral characteristic to estimate the carrier frequency offset.
In a feature of the invention, the method estimates the earlier frequency offset using a definition that the carrier frequency offset is the sum of a gross frequency offset and a partial offset. The gross frequency offset is a frequency offset of an amount that is an integer multiple of a unitary spacing on a frequency axis between two consecutive spectral lines in the spectrum of the periodic training sequence. The partial frequency offset is a frequency offset that is smaller, in absolute value, than half the unitary spacing on the frequency axis between two consecutive spectral lines in the spectrum of the employed periodic training sequence. The partial frequency offset is determined by the Chevillat method.
In another feature of the invention, the frequency shift due to the gross frequency offset is estimated by evaluating a mean-square error between the frequency characteristic computed for the overall channel and all possible characteristics obtained by successively shifting the ideal spectral characteristic by a unitary, discrete spacing until a minimum mean-square error is achieved. The number of unitary, discrete spacings away from the ideal spectral characteristic yields an estimate of the carrier-frequency offset.
In another feature of the invention, the frequency shift is obtained by performing four acts. In a first act from the ideal spectral characteristic, the method identifies a value equal to the largest number of consecutive discrete Fourier transform points for which the value of the spectral energy is essentially zero, thus defining a set of consecutive discrete Fourier transform points each having an associated magnitude and yielding, as a consequence, a width of a spectral window. In a second act, from the measured spectral characteristic, the method computes a sum of the magnitudes of all points in the set of consecutive discrete Fourier transform points found in the spectral window width determined in the first act, for all possible such windows. In a third act, the method determines the position of a set of consecutive discrete Fourier transform points, also known as the position of the spectral window, for which the sum of the magnitudes of the discrete Fourier transforms points is a minimum. In a fourth act, the method utilizes the amount by which the set of consecutive discrete Fourier transform points in the third act is shifted with respect to the set of consecutive discrete Fourier transform points in the first act to estimate the carrier-frequency offset.
In another feature of the invention, an equalizer is computed first, thus permitting a reliable calculation of the carrier frequency offset of the overall channel by employing an equalized characteristic.
In another feature of the invention, the logic medium is a computer-readable medium.
In another feature of the invention, the logic medium is a logic element having logic gates formed on a tangible medium.
In another feature of the invention, the frequency characteristic is a raised-cosine frequency characteristic.
An advantage of the invention is that significantly larger frequency-offset values can be acquired using the same cyclic preamble.
Another advantage of the invention, the method is simple to implement and useful in a variety of systems, for example, in HFC-CATV systems. where large carrier-frequency offset due to frequency stacking at the fiber node must be compensated, especially during upstream transmission in contention mode.